CBSE Class 10 – Page 143

RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS

January 5, 2022June 2, 2018 by Prasanna

RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 16 Probability MCQS

Other Exercises

Question 1.
Mark the correct alternative in each of the following:
If a digit is chosen at randon from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 1
Solution:
Total number of digits from 1 to 9 (n) = 9
Numbers which are odd (m) = 1, 3, 5, 7, 9 = 5

Question 2.
In Q. No. 1, the probability that the digit is even, is

Solution:
Total numbers of digits from 1 to 9 (n) = 9
Numbers which are even (m) = 2,4, 6, 8 = 4
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 4

Question 3.
In Q. No. 1, the probability that the digit is a multiple of 3 is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 5
Solution:
Total numbers of digits for 1 to 9 (n) = 9
Number divisible by 3 (m) = 3, 6, 9 = 3

Question 4.
If three coins are tossed simultaneously, then the probability of getting at least two heads, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 7
Solution:
Three coins are tossed simultaneously, then possible events will be (n) = 2 x 2 x 2 = 8
The results will be
(HHT), (HTH), (THH), (THT), (TTH), (HTT), (HHH), (TTT)
∴ Probability of getting at least two heads are

Question 5.
In a single throw of a die, the probability of getting a multiple of 3 is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 9
Solution:
A die is thrown, the possible number of events (n) = 6
Now multiple of 3 are 3, 6 which are 2
∴ m = 2

Question 6.
The probability of guessing the correct answer to a certain test questions is \(\frac { x }{ 12 }\) If the probability of not guessing the correct answer to this question is \(\frac { 2 }{ 3 }\) , then x =
(a) 2
(b) 3
(c) 4
(d) 6
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 11

Question 7.
A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 12
Solution:
In a bag, there are 3 green, 4 blue and 2 orange marbles
∴ Total marbles (n) = 3 + 4 + 2 = 9
No. of marbles which is not orange =3+4=7
∴m = 7

Question 8.
A number is selected at random from the . numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. The probability that the selected number is their average is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 14
Solution:

Question 9.
The probability of throwing a number greater than 2 with a fair dice is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 16
Solution:
∵ A dice has 6 numbers
∴ n = 6
Numbers greater than 2 are 3, 4, 5, 6
∴ m = 4

Question 10.
A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 18
Solution:
No. of card in a pack (n) = 52
A card is drawn at random
∴ No. of ace (m) =4

Question 11.
A number is selected from numbers 1 to 25. The probability that it is prime is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 20
Solution:
A number is selected from the numbers 1 to 25
Probability of prime number which are 2, 3, 5, 7, 11, 13, 17, 19, 23 = 9

Question 12.
Which of the following cannot be the probability of an event?
(a) \(\frac { 2 }{ 3 }\)
(b) -1.5
(c) 15%
(d) 0.7
Solution:
-1.5 cannot be the probability as it is always from 0 to 1 which is always positive (b)

Question 13.
If P (E) = 0.05, then P (not E) =
(a) – 0.5
(b) 0.5
(c) 0.9
(d) 0.95
Solution:
P (E) = 0.05
∵ P (E) + P (not E) = 1
∴ P (not E) = 1 – P (E) = 1 – 0.05 = 0.95 (d)

Question 14.
Which of the following cannot be the probability of occurrence of an event ?
(a) 0.2
(b) 0.4
(c) 0.8
(d) 1.6
Solution:
Probability of occurrence of an event = 1.6 (d)

Question 15.
The probability of a certain event is
(a) 0
(b) 1
(c) \(\frac { 1 }{ 2 }\)
(d) No existent
Solution:
Probability of a certain event = 1 (b)

Question 16.
The probability of an impossible event is
(a) 0
(b) 1
(c) \(\frac { 1 }{ 2 }\)
(d) Non – existent
Solution:
Probability of an impossible event = 0 (a)

Question 17.
Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 22
Solution:
No. of lottery tickets = 100
No. of tickets carrying prizes = 5
∴ Probability of ticket buying a prized one

Question 18.
A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5 ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 24

Solution:
Total numbers = 1 to 50 = 50
Numbers which are multiples of 3 or 5, are 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30, 33, 35, 36, 39, 40, 42, 45, 48, 50 = 23

Question 19.
A month is selected at random in a year. The probability that it is March or October, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 27
Solution:
No. of months in a year = 12
Probability of being March or October = \(\frac { 2 }{ 12 }\)

Question 20.
From the letters of the word “MOBILE”, a letter is selected. The probability that the letter is a vowel, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 29
Solution:
No. of total letters in the word MOBILE = 6
No, of vowels = o, i, e = 3

Question 21.
A die is thrown once. The probability of getting a prime number is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 31
Solution:
Prime number on a die are 2, 3, 5
∴ Probability of getting a prime number on the face of the die

Question 22.
The probability of getting an even, number, when a die is thrown once is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 33
Solution:
Even number on a die are 2, 4, 6 3
∴ Probability (P) = \(\frac { 3 }{ 6 }\) = \(\frac { 1 }{ 2 }\) (a)

Question 23.
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 34
Solution:
Number of discs in a box = 90
Numbered on it are 1 to 90
Prime numbers less than 23 are = 2, 3, 5, 7, 11, 13, 17, 19 = 8
Probability of a number being a prime less

Question 24.
The probablity that a number selected at random from the numbers 1, 2, 3, …..,15 is a multiple of 4, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 36
Solution:
Total outcomes = 15
(∵15 numbers are given)
Favourable outcomes for a multiple of 4 = 3 (i.e. 4, 8, 12)
∴ Probability of selecting a number which is

Question 25.
Two different coins are tossed simultaneously. The probability of getting at least one head is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 38
Solution:
When two different coins are tossed simultaneously, then total possibilities = 4,
i.e. (H, H), (H, T), (T, H), (T, T)
Number of favourable outcomes for at least one head = 3, i.e. (H, T), (T, H), (T, H).

Question 26.
If two different dice are rolled together, the probability of getting an even number
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 40
Solution:
Rolling two different dice,
Number of total events = 6 x 6 = 36
Number of even number on both dice are 22, 24, 26, 42, 44, 46, 62, 64, 66 = 9

Question 27.
A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 42
Solution:
Total outcomes of selecting a number from 30 numbers = 30
Favourable numbers (prime numbers) = 10,
i.e., (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
∴ Probability of selecting a prime number

Question 28.
A card is drawn at random from a pack of 52 cards. The probability that the drawn card is not an ace is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 44
Solution:
Total events = 52 cards
Probability of card which is not in ace Number of card = 52 – 4 = 48

Question 29.
A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3 the probability that |x| < 2 is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 46

Solution:
Total possible number of events (n) = 7
Now |x| <2
x < 2 or -x <2 ⇒ x > -2
∴ x
⇒ x = 1, 0 , -1, -2, -3 or x = -1, 0, 1 , 2, 3
∴ x = -1,0,1
∴ m = 3

Question 30.
If a number x is chosen from the numbers 1,2,3 and a number is selected from the numbers 1, 4, 9, then P (xy < 9)
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 49
Solution:
Numbers x = 1, 2, 3 and y = 1, 4, 9
Now xy= 1,4, 9, 2, 8, 18, 3, 12, 27 = 9
∴ n = 9
and xy < 9 are 1, 2, 3, 4, 8
∴m = 5

Question 31.
The probability that a non-leap year has 53 Sundays, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 51
Solution:
In a non leap years, number of days = 365 i.e. 52 weeks + 1 day
∴Probability of being 53 Sundays

Question 32.
In a single throw of a pair of dice, the probability of getting the sum a perfect square is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 53
Solution:
A pair of dice is thrown simultaneously
∴ No. of total events (n) = 6 x 6 = 36
Which are
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
∴Event whose sum is a perfect square are (1,3), (2, 2), (3, 1), (3, 6), (4, 5), (5, 4), (6, 3)
∴m = 7
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 54

Question 33.
What is the probability that a non-leap year has 53 Sundays ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 55
Solution:
No. of days in a non leap year = 365
∴No. of days more than complete weeks = 1 day
∴ Probability of 53 Sundays in a non-leap year

Question 34.
Two numbers ‘a’ and ‘6’ are selected successively without replacement in that order from the integers 1 to 10. The probability that \(\frac { a }{ b }\) is an integer, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 57
Solution:
a and b are two number to be selected from the integers = 1 to 10 without replacement of a and b
i.e., 1 to 10 = 10
and 2 to 10 = 9
No. of ways = 10 x 9 = 90
Probability of \(\frac { a }{ b }\) where it is an integer
∴ Possible event will be
= (2, 2), (3, 3), (4, 2), (4, 4), (5, 5), (6, 2), (6, 3), (6, 6), (7, 7), (8, 2), (8, 4), (8, 8), (9, 3), (9, 9), (10, 2), (10, 5), (10, 10), = 17
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 58

Question 35.
Two dice are rolled simultaneously. The probability that they show different faces is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 59
Solution:
Two dice are rolled simultaneously
∴ No. of total events = 62 = 36
∴ No. of different face can be
= 36 – (same faces)
Same face are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6) = 6
∴ 36-6 = 30

Question 36.
What is the probability that a leap year has 52 Mondays ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 61
Solution:
No. of days in a leap year = 366
No. of Mondays = 52
Extra days = 366 – 52 x 7
= 366 – 364= 2
∴ Remaining days in the week = 7-2 = 5
∴Probability of being 52 Mondays in the leap

Question 37.
If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 63
Solution:
Total number of two digit numbers are 10 to 99
= 99 – 9 = 90
Multiples of 3 will be 12, 15, 18, 21,…. 99
= 33 – 3 = 30

Question 38.
Two dice are thrown together. The probability of getting the same number on both dice is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 65
Solution:
2 dice are thrown together
∴Number of total outcomes = 6 x 6 = 36
Number which should come together are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
= 6 pairs

Question 39.
In a family of 3 children, the probability of having at least one boy is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 67
Solution:
Number of children in a family = 3
There can be,
bbb.bbg, bgg and ggg
∴Probability of a family having atleast one boy = \(\frac { 3}{ 4 }\) (d)

Question 40.
A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is
RD Sharma Class 10 Solutions Chapter 16 Probability Ex MCQS 69
Solution:
Total number of outcomes = 25
The number which is divisible by both 2 and 3 are 6, 12, 18, 24.
Number of favourable outcomes = 4 Probability of number which is divisible by both 2 and 3 = \(\frac { 4 }{ 25 }\) (c)

Hope given RD Sharma Class 10 Solutions Chapter 16 Probability MCQS are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

January 5, 2022June 2, 2018 by Prasanna

RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

Other Exercises

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : (1 – 4)
Question 1.
x – 3y = 3
3x – 9y = 2 (C.B.S.E. 1994)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 1

Question 2.
2x + y = 5
4x + 2y = 10 (C.B.S.E. 1995C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 2

Question 3.
3x – 5y = 20
6x – 10y = 40 (C.B.S.E. 1993)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 3

Question 4.
x – 2y = 8
5x – 10y = 10 (C.B.S.E. 1993)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 5

Find the value of k for which the following system of equations has a unique solution: (5 – 8)
Question 5.
kx + 2y = 5
3x + y = 1 (C.B.S.E. 1990C, 92C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 6

Question 6.
4x + ky + 8 = 0
2x + 2y + 2 = 0 [NCERT]
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 7

Question 7.
4x – 5y = k
2x – 3y = 12
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 9

Question 8.
x + 2y = 3
5x + ky + 7 = 0
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 10

Find the value of k for which each of the following systems of equations have infinitely many solution : (9 – 19)
Question 9.
2x + 3y – 5 = 0
6x + ky – 15 = 0 (C.B.S.E. 1991)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 11

Question 10.
4x + 5y = 3
kx + 15y = 9 (C.B.S.E. 1990C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 12

Question 11.
kx – 2y + 6 = 0
4x – 3y + 9 = 0
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 13

Question 12.
8x + 5y = 9
kx + 10y = 18 (C.B.S.E. 1999)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 15

Question 13.
2x – 3y = 7
(k + 2) x + (2k + 1) y = 3 (2k – 1) (C.B.S.E. 1999)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 16

Question 14.
2x + 3y = 2
(k + 2)x + (2k + 1) y = 2 (k – 1) (C.B.S.E. 2000, 2003)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 18

Question 15.
x + (k + 1) y = 4
(k + 1) x + 9y = 5k + 2 (C.B.S.E. 2000C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 20

Question 16.
kx + 3y = 2k + 1
2(k+ 1) x + 9y = 7k + 1 (C.B.S.E. 2000C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 21

Question 17.
2x + (k – 2) y = k
6x + (2k – 1) y = 2k + 5 (C.B.S.E. 2000C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 23

Question 18.
2x + 3y = 7
(k + 1) x + (2k – 1)y = 4k + 1 (C.B.S.E. 2001)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 25

Question 19.
2x + 3y = k
(k – 1) x + (k + 2) y = 3k (C.B.S.E. 2001)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 26

Find the value of k for which the following system of equations has no solution : (20 – 25) :
Question 20.
kx – 5y = 2
6x + 2y = 1 (C.B.S.E. 1994C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 27

Question 21.
x + 2y = 0
2x + ky = 5 (C.B.S.E. 1993C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 29

Question 22.
3x – 4y + 7 = 0
kx + 3y – 5 = 0 (C.B.S.E. 1996)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 30

Question 23.
2x – ky + 3 = 0
3x + 2y – 1 = 0 (C.B.S.E. 1996)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 32

Question 24.
2x + ky = 11
5x – 7y = 5 (C.B.S.E. 1995)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 34

Question 25.
kx + 3y = 3
12x + ky = 6
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 35

Question 26.
For what value of k, the following system of equations will be inconsistant ?
4x + 6y = 11
2x + ky = 1 (C.B.S.E. 1994C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 37

Question 27.
For what value of a, the system of equations
αx + 3y = α – 3
12x + αy = α
will have no solution. (C.B.S.E. 2003)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 38

Question 28.
Find the value of k for which the system
kx + 2y = 5
3x + y = 1
has (i) a unique solution, and (ii) no solution.
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 40
k = 6

Question 29.
Prove that there is a value of c (≠ 0) for which the system
6x + 3y = c – 3
12x + cy = c
has infinitely many solutions. Find this value.
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 41

Question 30.
Find the values of k for which the system
2x + k y = 1
3x – 5y = 7
will have (i) a unique solution, and (ii) no solution.
Is there a value of k for which the system has infinitely many solutions?
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 42

Question 31.
For what value of k, the following system of equations will represent the coincident lines ?
x + 2y + 7 = 0
2x + ky + 14 = 0 (C.B.S.E. 1992)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 43

Question 32.
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n (C.B.S.E. 1991C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 44

Question 33.
Determine the values of a and b so that the following system of linear equations have infinitely many solutions ?
(2a – 1) x + 3y – 5 = 0
3x + (b – 1) y – 2 = 0 (C.B.S.E. 2001C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 45

Question 34.
Find the values of a and b for which the following system of linear equations has infinite number of solutions :
2x – 3y = 7
(a + b) x – (a + b – 3) y = 4a + b (C.B.S.E. 2002)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 47

Question 35.
Find the values of p and q for which the following system of linear equations has infinite number of solutions:
2x + 3y = 9
(p + q) x + (2p – q) y = 3 (p + q + 1)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 48

Question 36.
Find the value of a and b for which the following system of equations has infinitely many solutions :
(i) (2a – 1) x – 3y = 5
3x + (b – 2) y = 3 (C.B.S.E. 2002C)
(ii) 2x – (2a + 5) y = 5
(2b + 1) x – 9y = 15 (C.B.S.E. 2002C)
(iii) (a – 1) x + 3y = 2
6x + (1 – 2b) y = 6 (C.B.S.E. 2002C)
(iv) 3x + 4y = 12
(a + b) x + 2 (a – b) y = 5a – 1 (C.B.S.E. 2002C)
(v) 2x + 3y = 7
(a – b) x + (a + b) y = 3a + b – 2
(vi) 2x + 3y – 7 = 0 [CBSE 2010]
(a – 1) x + (a + 1) y = (3a – 1)
(vii) 2x + 3y = 7
(a – 1) x + (a + 2) y = 3a [CBSE 2010]
(viii) x + 2y = 1
(a – b) x + (a + b) y = a + b – 2 [NCERT Exemplar]
(ix) 2x + 3y = 7
2ax + ay = 28 – by [NCERT Exemplar]
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 50

Question 37.
For which value(s) of λ, do the pair of linear equations λx + y = λ² and x + λy = 1 have
(i) no solution ?
(ii) infinitely many solutions ?
(iii) a unique solutions ? [NCERT Exemplar]
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 62

Hope given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS

January 5, 2022June 1, 2018 by Prasanna

RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 16 Probability VSAQS

Other Exercises

Question 1.
Cards each marked with one of the numbers 4, 5, 6, …….. 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box what is the probability of getting an even number ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 1

Question 2.
One card is drawn from a well shuffled deck of 52 playing cards. What is the probability of getting a non-face card ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 2

Question 3.
A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 3

Question 4.
A die is thrown once. What is the probability of getting a prime number?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 4

Question 5.
A die is thrown once. What is the probability of getting a number lying between 2 and 6 ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 5

Question 6.
A die is thrown once. What is the probability of getting an odd number ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 6

Question 7.
If \(\bar { E }\) denoted the complement or negation of an even E, what is the value of P(E) + P(\(\bar { E }\))?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 7

Question 8.
One card is drawn at random from a well shuffled deck of 52 cards. What is the probability of getting an ace ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 8

Question 9.
Two coins are tossed simultaneously. What is the probability of getting at least one head ?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 9

Question 10.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 10

Question 11.
From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a black queen.[C.B.S.E. 2008]
Solution:

RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 12

Question 12.
A die is thrown once. Find the probability of getting a number less than 3. [CBSE 2008]
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 13

Question 13.
Two coines are tossed simultaneously. Find the probability of getting exactly one head. [CBSE 2009]
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 16

Question 14.
A die is thrown once. What is the probability of getting a number greater than 4 ? [CBSE 2010]
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 17

Question 15.
What is the probability that a number selected at random from the numbers 3, 4, 5,…, 9 is a multiple of 4 ? [CBSE 2010]
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 18

Question 16.
A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a consonant.
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 19

Question 17.
A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red? [CBSE 2017]
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 20

Question 18.
A number is chosen at random from the numbers, -3, -2, -1, 0,1, 2, 3. What will be the probability that the square of this number is less than or equal tori?
Solution:
RD Sharma Class 10 Solutions Chapter 16 Probability Ex VSAQS 21

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RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2

January 5, 2022June 1, 2018 by Prasanna

RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2

Other Exercises

Question 1.
Suppose you drop a tie at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter 1 m?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 1
Solution:

Question 2.
In the accompanying diagram a fair spinner is placed at the centre O of the circle. Diameter AOB and radius OC divide the circle into three rigions labelled X, Y and Z. If ∠BOC = 45°. What is the probability that the spinner will land in the region X?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 3
Solution:

Question 3.
A target shown in the figure consists of three concentric circles of radii 3, 7 and 9 cm respectively. A dart is thrown and lands on the target. What is the probability that the dart will land on the shaded region ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 6
Solution:

Question 4.
In the figure, points A, B, C and D arc the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior o’ square ABCD. What is the probability that the point will be chosen from th; shaded region ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 8
Solution:

Question 5.
In the figure, JKLM is a square with sides of length 6 units. Points A and B are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of ∆JAB?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 10
Solution:

Question 6.
In the figure, a square dart board is shown. The length of a side of the larger square is 1.5 times the length of a side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square ?
RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 13
Solution:

Hope given RD Sharma Class 10 Solutions Chapter 16 Probability Ex 16.2 are helpful to complete your math homework.

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RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4

January 5, 2022June 1, 2018 by Prasanna

RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4

Other Exercises

Solve each of the following systems of equations by the method of cross multiplication.
Question 1.
x + 2y + 1 = 0
2x – 3y – 12 = 0 (C.B.S.E. 1992)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 1

Question 2.
3x + 2y + 25 = 0
2x + y + 10 = 0 (C.B.S.E. 1992)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 2

Question 3.
2x + y = 35
3x + 4y = 65 (C.B.S.E. 1993)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 4

Question 4.
2x – y = 6
x – y = 2 (C.B.S.E. 1994)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 5

Question 5.
\(\frac { x+y }{ xy } =2,\quad \frac { x-y }{ xy } =6\)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 6

Question 6.
ax + by = a – b
bx – ay = a + b
Solution:
ax + by = a – b
bx – ay = a + b
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 9

Question 7.
x + ay = b
ax – by = c
Solution:
x + ay = b
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 11

Question 8.
ax + by = a²
bx + ay = b²
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 13

Question 9.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 15
Solution:

Question 10.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 18
Solution:

Question 11.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 21
Solution:

Question 12.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 24
Solution:

Question 13.
\(\frac { x }{ { a } } +\frac { y }{ b } =a+b\)
\(\frac { x }{ { { a }^{ 2 } } } +\frac { y }{ { b }^{ 2 } } =2\)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 28

Question 14.
\(\frac { x }{ { { a } } } =\frac { y }{ { b } }\)
ax + by = a² + b²
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 31

Question 15.
2ax + 3by = a + 2b
3ax + 2by = 2a + b
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 34

Question 16.
5ax + 6by = 28
3ax + 4by = 18
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 37

Question 17.
(a + 2b) x + (2a – b) y = 2
(a – 2b) x + (2a + b) y = 3
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 39

Question 18.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 41
Solution:

Question 19.
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 46
Solution:

Question 20.
(a – b) x + (a + b) y = 2a² – 2b²
(a + b) (x + y) = 4ab
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 52

Question 21.
a²x + b²y = c²
b²x + a²y = d²
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 56

Question 22.
ax + by = \(\frac { a + b }{ 2 }\)
3x + 5y = 4
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 57

Hence x = \(\frac { 1 }{ 2 }\) , y = \(\frac { 1 }{ 2 }\)

Question 23.
2 (ax – by) + a + 4b = 0
2 (bx + ay) + b – 4a = 0 (C.B.S.E. 2004)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 59

Question 24.
6 (ax + by) = 3a + 2b
6 (bx – ay) = 3b – 2a (C.B.S.E. 2004)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 61

Question 25.
\(\frac { { a }^{ 2 } }{ x } -\frac { { b }^{ 2 } }{ y } =0\)
\(\frac { { a }^{ 2 }b }{ x } -\frac { { b }^{ 2 }a }{ y } =a+b\quad ,\quad x,y\quad \neq 0\)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 63

Question 26.
mx – ny = m² + n²
x + y = 2m (C.B.S.E. 2006C)
Solution:
RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 65